Solve 2(x-1/2x)(x+1/x)(2x-3)

$$2 ( x - \frac { 1 } { 2 x } ) ( x + \frac { 1 } { x } ) ( 2 x - 3 )$$

Evaluate

$$\frac{\left(2x-3\right)\left(2x^{2}-1\right)\left(x^{2}+1\right)}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2x}{2x}.

$$2\left(\frac{x\times 2x}{2x}-\frac{1}{2x}\right)\left(x+\frac{1}{x}\right)\left(2x-3\right)$$

Since \frac{x\times 2x}{2x} and \frac{1}{2x} have the same denominator, subtract them by subtracting their numerators.

$$2\times \frac{x\times 2x-1}{2x}\left(x+\frac{1}{x}\right)\left(2x-3\right)$$

Do the multiplications in x\times 2x-1.

$$2\times \frac{2x^{2}-1}{2x}\left(x+\frac{1}{x}\right)\left(2x-3\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$2\times \frac{2x^{2}-1}{2x}\left(\frac{xx}{x}+\frac{1}{x}\right)\left(2x-3\right)$$

Since \frac{xx}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$2\times \frac{2x^{2}-1}{2x}\times \frac{xx+1}{x}\left(2x-3\right)$$

Do the multiplications in xx+1.

$$2\times \frac{2x^{2}-1}{2x}\times \frac{x^{2}+1}{x}\left(2x-3\right)$$

Express 2\times \frac{2x^{2}-1}{2x} as a single fraction.

$$\frac{2\left(2x^{2}-1\right)}{2x}\times \frac{x^{2}+1}{x}\left(2x-3\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{2x^{2}-1}{x}\times \frac{x^{2}+1}{x}\left(2x-3\right)$$

Multiply \frac{2x^{2}-1}{x} times \frac{x^{2}+1}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x^{2}-1\right)\left(x^{2}+1\right)}{xx}\left(2x-3\right)$$

Express \frac{\left(2x^{2}-1\right)\left(x^{2}+1\right)}{xx}\left(2x-3\right) as a single fraction.

$$\frac{\left(2x^{2}-1\right)\left(x^{2}+1\right)\left(2x-3\right)}{xx}$$

Multiply x and x to get x^{2}.

$$\frac{\left(2x^{2}-1\right)\left(x^{2}+1\right)\left(2x-3\right)}{x^{2}}$$

Apply the distributive property by multiplying each term of 2x^{2}-1 by each term of x^{2}+1.

$$\frac{\left(2x^{4}+2x^{2}-x^{2}-1\right)\left(2x-3\right)}{x^{2}}$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$\frac{\left(2x^{4}+x^{2}-1\right)\left(2x-3\right)}{x^{2}}$$

Apply the distributive property by multiplying each term of 2x^{4}+x^{2}-1 by each term of 2x-3.

$$\frac{4x^{5}-6x^{4}+2x^{3}-3x^{2}-2x+3}{x^{2}}$$

Expand

$$4x^{3}-6x^{2}+2x-3-\frac{2}{x}+\frac{3}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2x}{2x}.

$$2\left(\frac{x\times 2x}{2x}-\frac{1}{2x}\right)\left(x+\frac{1}{x}\right)\left(2x-3\right)$$

Since \frac{x\times 2x}{2x} and \frac{1}{2x} have the same denominator, subtract them by subtracting their numerators.

$$2\times \frac{x\times 2x-1}{2x}\left(x+\frac{1}{x}\right)\left(2x-3\right)$$

Do the multiplications in x\times 2x-1.

$$2\times \frac{2x^{2}-1}{2x}\left(x+\frac{1}{x}\right)\left(2x-3\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$2\times \frac{2x^{2}-1}{2x}\left(\frac{xx}{x}+\frac{1}{x}\right)\left(2x-3\right)$$

Since \frac{xx}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$2\times \frac{2x^{2}-1}{2x}\times \frac{xx+1}{x}\left(2x-3\right)$$

Do the multiplications in xx+1.

$$2\times \frac{2x^{2}-1}{2x}\times \frac{x^{2}+1}{x}\left(2x-3\right)$$

Express 2\times \frac{2x^{2}-1}{2x} as a single fraction.

$$\frac{2\left(2x^{2}-1\right)}{2x}\times \frac{x^{2}+1}{x}\left(2x-3\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{2x^{2}-1}{x}\times \frac{x^{2}+1}{x}\left(2x-3\right)$$

Multiply \frac{2x^{2}-1}{x} times \frac{x^{2}+1}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x^{2}-1\right)\left(x^{2}+1\right)}{xx}\left(2x-3\right)$$

Express \frac{\left(2x^{2}-1\right)\left(x^{2}+1\right)}{xx}\left(2x-3\right) as a single fraction.

$$\frac{\left(2x^{2}-1\right)\left(x^{2}+1\right)\left(2x-3\right)}{xx}$$

Multiply x and x to get x^{2}.

$$\frac{\left(2x^{2}-1\right)\left(x^{2}+1\right)\left(2x-3\right)}{x^{2}}$$

Apply the distributive property by multiplying each term of 2x^{2}-1 by each term of x^{2}+1.

$$\frac{\left(2x^{4}+2x^{2}-x^{2}-1\right)\left(2x-3\right)}{x^{2}}$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$\frac{\left(2x^{4}+x^{2}-1\right)\left(2x-3\right)}{x^{2}}$$

Apply the distributive property by multiplying each term of 2x^{4}+x^{2}-1 by each term of 2x-3.

$$\frac{4x^{5}-6x^{4}+2x^{3}-3x^{2}-2x+3}{x^{2}}$$